Additional file1

Method for the calculation of dissociation constant values

The formation of complexes between recombinant proteins and radiolabeled double stranded oligonucleotide probes was measured as a function of protein concentration employing Eq. (1),

(1)

where F is the fraction of DNA probe in DNA-protein complexes, Sx is the amount of radioactivity in the shifted DNA-protein complex at protein concentration x, S0 is the corresponding radioactivity at x = 0, and Sf is the average amount of radioactivity when F becomes independent of x, i.e., when titration end point has been reached. For an accurate determination of Sf values for each experiment, Sx values were plotted for each x concentration of recombinant polypeptide tested. Then, the polynomial function that best describes the curve behavior was determined as follows:

(2)

Where ln Sxis the natural logarithm of Sx, an is the coefficient, n is the equation degree, and E is the residual error in the regression analysis [1]. The least square regression analysis was performed for fitness analysis. The degree of Eq. (2) determined in this work for both rEhTBP and rEhTRF1 and all DNA probes tested was n = 2. The statistical Student’s t-test (t) for each an was estimated with the next equation:

(3)

Where j has a value between 0 and n, and San is the standard deviation of an coefficient. The difference (an − 0) was considered as significant whether the Student’s t-test probability P(t) was lower than 0.05 [1].

After the calculation of coefficients of Eq. (2) for each experiment, the concentrations xmax for rEhTBP or rEhTRF1 for all the probes tested corresponding to the maximum of curves, were determined by deriving Eq. (2) and solving it for zero value.

(4)

Then values of xmax for Eq. (2) were used to obtain the Sf values and F was calculated with Eq. (1) for each x concentration of rEhTBP and rEhTRF1 used.

For the estimation of the molar ratios of total rEhTBP/DNA-probe and total rEhTRF1/DNA-probe when F = 1, the fractions of active rEhTBP and rEhTRF1 polypeptides binding to each of the DNA probes tested (active unbound plus active bound proteins) were determined assuming a binding stoichiometry of 1 [2]. Next, F was plotted as a function of total protein to DNA probe molar ratios. Following the procedure followed for Eq. (2), the ln F was fitted as a polynomial function of the molar ratios of total rEhTBP/DNA-probe or rEhTRF1/DNA-probe by the least square method. The maximum of these curves were determined as before. For an F value of 1 (i.e. the saturating point), the reciprocal of the x intercept was multiplied by the total concentration of rEhTBP or rEhTRF1 in order to get the total fraction of active rEhTBP or rEhTRF1 in reaction mixtures. This value was named (x/DNA probe)max and it corresponds to a value of F = 1 [2].

For determining the Confidence Intervals (CI) of predictions obtained for the polynomial functions, the value Yp ± CI was used, being Yp the predicted value by the function for an x value. CI is defined by Eq. (5)

(5)

Where t(0.975, gl) is the Student’s t-test for 0.975 percentile, and gl the degrees of freedom; X’ is the vector of the values raised to the transposed X vector, R-1 corresponds to the inverse of the regression matrix, and 1/2 is the residual variance.

For the calculation of dissociation constants KD of DNA-protein complexes, we used the Eq. (6) as described [1, 3].

(6)

Where P corresponds to the uncomplexed amount of active rEhTBP or rEhTRF1 polypeptides and is related to the total concentration (PT)of total active rEhTBP or rEhTRF1 by Eq. (7)

(7)

PD is the concentration of rEhTBP or rEhTRF1 in the DNA-protein complexes. Since Eq. (6) is a hyperbolic function, then 1/F should fit to a linear function of the reciprocal of P, and the slope of this line corresponds to KD. Next, these two variables were fitted by means of a robust regression method [1, 3]that avoided the deleterious effect of data outliers on KD values. Calculation of coefficients and variances were performed by programming iterative algorithms that used least square estimates as initial values [1, 3]. The apparent association equilibrium constant Ka is defined as the reciprocal of KD.

Dissociation constants of rEhTBP and rEhTRF1 for the different TATA variants

The dissociation constants of rEhTBP and rEhTRF1 for the different TATA variants were determined as described [1, 3]. First, EMSA experiments were performed to quantify the amount of radioactivity (Sx) in the DNA-protein complexes formed with increasing amounts of purified rEhTBP or rEhTRF1 polypeptides (Fig. S1, A to J). Then, the natural logarithms of Sxvalues (ln Sx) were plotted as a function of the different protein concentrations tested (Fig. S1, A to I). Experimental points were fitted to a second-degree polynomial function that best describes the mathematical relationship of ln Sxas a function of x (Fig. S1, A to I; Tables S1 and S2). To determine the average amount of radioactivity Sf in the DNA-protein complexes at the titration end point, Eq. (4) was used to calculate the x value (xmax) that corresponds to the maximum of equation. Then, this xmax value was substituted in Eq. (2) to determine the Sf value. Next, F values were determined for each protein concentration used using Eq. (1) and the natural logarithms of F values were plotted as a function of the total protein/DNA probe molar ratios. These points were fitted to a second-degree polynomial function as well (Tables S1 and S2; see Fig. 2H and K as graph examples). The values of protein/DNA probe molar ratios were determined by deriving these equations to obtain the maximum of curves that correspond to an F value of 1. Finally, we obtained the reciprocal values of F to plot them as a function of the reciprocal values of concentration P (the uncomplexed amount of active rEhTBP or rEhTRF1 polypeptides), which were calculated with Eq. (7). The relationship of F and P is described by Eq. (6). The plots obtained were lineal (see Fig. 2, I and L as examples) and its slope corresponds to the KD value. The dissociation constants obtained for each TATA variant studied are shown in Table 1. The KD values of rEhTBP for all the TATA variants analyzed varied between (1.69±1.37) x 10-12 M and (3.98±0.16) x 10-11 M, while the KD values of rEhTRF1 for all TATA variants were between (3.98±1.96) x 10-12 M and (5.29±0.98) x 10-11 M. Remarkably, rEhTBP did not show DNA-binding affinity for the cAcTTAAA(9) variant.

References

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  2. Coleman RA, Pugh BF. Evidence for functional binding and stable sliding of the TATA binding protein on nonspecific DNA. J Biol Chem. 1995;270:13850–13859.
  3. Castañon-Sanchez CA, Luna-Arias JP, de Dios-Bravo G, Herrera-Aguirre ME, Olivares-Trejo JJ, Orozco E, Hernandez JM. Entamoeba histolytica: A unicellular organism containing two active genes encoding for members of the TBP family. Protein Expr Purif. 2010;70:48-59.